On weak filter convergence and the radon-riesz type theorem

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• 作者：Lingxin BAO ^{bolingxmu@sina.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：statistical convergence ; filter convergence ; Radon-Riesz property ; Banach space
• 刊名：Acta Mathematica Scientia
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：36
• 期：1
• 页码：215-219
• 全文大小：273 K

文摘

The author shows a characterization of a (unbounded) weakly filter convergent sequence which is parallel to that every weakly null sequence (x_n) in a Banach space admits a norm null sequence (y_n  ) with708337c04fd" title="Click to view the MathML source">y_n∈co(x_k)_k≥n$y_n\in \text{co}{\left(x_k\right)}_k\ge n$ for alln∈ℕ$n\in \mathbb{N}$. A version of the Radon-Riesz type theorem is also proved within the frame of the filter convergence.